Analysis of ecological context variables and regression models for prediction the relationship (slope) between lake water level and cumulative precipitation deviation using 40 Lake data set generated on Feb. 27 2019. These analyses are driven by semi-informed decisions about what ecological context variables may be important factors influencing water level changes in lakes and their response precipitation.
Data in this analysis involves slope values from 40 lakes.
The lakes were chosen by the following criteria:
The ecological context variables used to understand the variation in the slope of the relationships among lakes between water levels and precip seen above included the following variables slope, MaxDepth, W_PERM, W_DARCY, cond, elevation_difference, Area, r_forest. Slope is the response variable. Forest land type was choose for the land-use variable because it is strongly correlated with other variables. We also choose to use land-use characteristics calculated for the riparian zone (30m buffer) around the lake.
We have tested a variety of model selection approaches to explain the variation in among lake slopes and ecological context variables including black box approaches such as random forest. For easy of interpretation, we have choosen to rely on linear models. Model selection was conducted using the glmulti package to quanitify the best 0:4 parameter models including the potential for two-way interactions. We also limited the model to 4 predictor variables which would could include the interaction between two variables and an additional variable (3 parameters) or 4 parameters if no interactions included due to sample size concerns and overfitting the data.
| model | aicc |
|---|---|
| slope ~ 1 + W_DARCY + cond + elevation_difference + cond:W_DARCY | 63.14421 |
| slope ~ 1 + W_DARCY + elevation_difference + r_forest + r_forest:W_DARCY | 65.78285 |
| slope ~ 1 + W_DARCY + cond + cond:W_DARCY | 67.41354 |
| slope ~ 1 + W_DARCY + cond + Area + cond:W_DARCY | 68.59125 |
| slope ~ 1 + cond + elevation_difference + elevation_difference:cond | 68.85866 |
| slope ~ 1 + MaxDepth + W_DARCY + cond + cond:W_DARCY | 69.55145 |
| slope ~ 1 + W_PERM + W_DARCY + cond + cond:W_DARCY | 70.16676 |
| slope ~ 1 + MaxDepth + cond + elevation_difference + elevation_difference:cond | 70.17875 |
| slope ~ 1 + W_DARCY + Area + r_forest + r_forest:W_DARCY | 71.03460 |
| slope ~ 1 + cond + elevation_difference | 71.19999 |
| slope ~ 1 + W_DARCY + cond + elevation_difference + elevation_difference:cond | 71.31015 |
| slope ~ 1 + elevation_difference | 71.98504 |
| slope ~ 1 + MaxDepth + cond + elevation_difference | 72.75802 |
| slope ~ 1 + cond + elevation_difference + Area | 72.90693 |
| slope ~ 1 + elevation_difference + Area | 73.25866 |
| slope ~ 1 + W_DARCY + cond + elevation_difference | 73.42975 |
| slope ~ 1 + elevation_difference + r_forest | 73.55986 |
| slope ~ 1 + MaxDepth + elevation_difference | 73.63163 |
| slope ~ 1 + cond + elevation_difference + r_forest | 73.81450 |
| slope ~ 1 + W_PERM + cond + elevation_difference | 73.82182 |
##
## Call:
## lm(formula = slope ~ elevation_difference + cond * W_DARCY, data = dat_input)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8645 -0.2267 -0.0636 0.2278 1.0575
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.112e+00 2.757e-01 4.034 0.000283 ***
## elevation_difference 1.564e-02 6.021e-03 2.597 0.013652 *
## cond -1.222e-03 1.182e-03 -1.034 0.308196
## W_DARCY 1.623e-03 8.631e-04 1.880 0.068445 .
## cond:W_DARCY -2.355e-05 6.403e-06 -3.677 0.000785 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4749 on 35 degrees of freedom
## Multiple R-squared: 0.5133, Adjusted R-squared: 0.4577
## F-statistic: 9.228 on 4 and 35 DF, p-value: 3.361e-05
Comparison of the distrubtion of values and predicted slopes for the modeled population (observed) and extrapolation population (exptrapolation) for which the general model was used to extrapolate slopes.
While it is clear that we are missing some of the extreme values in our model population (lakes used to build the model), it does not appear to influence the predictive slopes substantually. The extrapolated slopes (n = 455) are largely bounded by the slopes observed in the modeled population.
We also ran the models using forest landuse data instead of conductivity because it performed only slightly worse and may allow extrapolation in lakes without conductivity data.
##
## Call:
## lm(formula = slope ~ elevation_difference + cond * W_DARCY, data = dat_input)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8645 -0.2267 -0.0636 0.2278 1.0575
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.112e+00 2.757e-01 4.034 0.000283 ***
## elevation_difference 1.564e-02 6.021e-03 2.597 0.013652 *
## cond -1.222e-03 1.182e-03 -1.034 0.308196
## W_DARCY 1.623e-03 8.631e-04 1.880 0.068445 .
## cond:W_DARCY -2.355e-05 6.403e-06 -3.677 0.000785 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4749 on 35 degrees of freedom
## Multiple R-squared: 0.5133, Adjusted R-squared: 0.4577
## F-statistic: 9.228 on 4 and 35 DF, p-value: 3.361e-05
Comparison of the distrubtion of values and predicted slopes for the modeled population (observed) and extrapolation population (exptrapolation) for which the general model was used to extrapolate slopes.